The Stabilization of a Star‐Shaped Network With Moving Boundary

ABSTRACT In this paper, we study the stabilization of a star‐shaped network of strings with moving boundary. The network consists of three connected arcs through a single node. Each arc is governed by the wave equation. Disturbances are applied only at the two endpoints of the star‐shaped network. At the central node, the arcs are coupled by Kirchhoff conditions in such a way that the energy is non‐increasing. Using the multiplier method, we prove that the system is polynomially stable and the decay rates depend on the range of the parameter .